2019/12/09 by Nour Eddine Askour, Askour, Nour eddine, Mohamed Bouaouid +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1912.04417
openalex publication_date 2019/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of the present paper is three folds. For a reproducing kernel Hilbert\nspace \A (R.K.H.S) and a \σ-finite measure space\n(M1,d\μ1) for which the corresponding L2-space is a separable\nHilbert space, we first build an isometry of Bargmann type as an integral\ntransform from L2(M1,d\μ1) into \A. Secondly, in the\ncase where there exists a \σ-finite measure space (M2,d\μ2) such\nthat the Hilbert space L2(M2,d\μ2) is separable and\n\A\⊂ L2(M2,d\μ2) the inverse isometry is also given\nin an explicit form as an integral transform. As consequence, we recover some\nclassical isometries of Bargmann type. Thirdly, for the classical Dirichlet\nspace as R.K.H.S, we elaborate a new isometry of Bargmann type. Furthermore,\nfor this Dirichlet space, we give a new characterization, as harmonic space of\na single second order elliptic partial differential operator for which, we\npresent some spectral properties. Finally, we extend the same results to a\nclass of generalized Bergman-Dirichlet space.\n